Question
Answer
$$\dfrac{9\sqrt{30}}{18\sqrt{45}}=\dfrac{\sqrt{6}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9\sqrt{30}}{18\sqrt{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9\sqrt{30}}{18\sqrt{45}}\frac{\sqrt{45}}{\sqrt{45}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{135\sqrt{6}}{810} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{6}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{45}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 9 \sqrt{30} } \cdot \sqrt{45} = 135 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 18 \sqrt{45} } \cdot \sqrt{45} = 810 $$ |
| ③ | Divide both numerator and denominator by 135. |
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